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Optical Polarimetry for Fundamental Physics

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Optical Polarimetry for Fundamental Physics universe Review Optical Polarimetry for Fundamental Physics Guido Zavattini 1,2,* and Federico Della Valle 3,4 1 Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via G. Saragat 1, I-44122 Ferrara, Italy 2 INFN, Sezione di Ferrara, Via G. Saragat 1, I-44122 Ferrara, Italy 3 Dipartimento di Scienze Fisiche, della Terra e dell’Ambiente, Università di Siena, Via Roma 56, I-53100 Siena, Italy; [email protected] 4 INFN, Sezione di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy * Correspondence: [email protected] Abstract: Sensitive magneto-optical polarimetry was proposed by E. Iacopini and E. Zavattini in 1979 to detect vacuum electrodynamic non-linearity, in particular Vacuum Magnetic Birefringence (VMB). This process is predicted in QED via the fluctuation of electron–positron virtual pairs but can also be due to hypothetical Axion-Like Particles (ALPs) and/or MilliCharged Particles (MCP). Today ALPs are considered a strong candidate for Dark Matter. Starting in 1992 the PVLAS collaboration, financed by INFN, Italy, attempted to measure VMB conceptually following the original 1979 scheme based on an optical cavity permeated by a time-dependent magnetic field and heterodyne detection. Two setups followed differing basically in the magnet: the first using a rotating superconducting 5.5 T dipole magnet at the Laboratori Nazionali di Legnaro, Legnaro, Italy and the second using two rotating permanent 2.5 T dipole magnets at the INFN section of Ferrara. At present PVLAS is the experiment which has set the best limit in VMB reaching a noise floor within a factor 7 of the predicted QED signal: Dn(QED) = 2.5 × 10−23 @ 2.5 T. It was also shown that the noise floor was due to the optical cavity and a larger magnet is the only solution to increase the signal to noise ratio. The PVLAS experiment ended at the end of 2018. A new effort, VMB@CERN, which plans to use a spare Citation: Zavattini, G.; Della Valle, F. LHC dipole magnet at CERN with a new modified optical scheme, is now being proposed. In this Optical Polarimetry for Fundamental review, a detailed description of the PVLAS effort and the comprehension of its limits leading to a Physics. Universe 2021, 7, 252. new proposal will be given. https://doi.org/10.3390/ universe7070252 Keywords: optical polarimetry; magneto-optic effects; optical tests of quantum electrodynamics Academic Editors: Janos Polonyi and Freya Blekman Received: 1 June 2021 1. Introduction Accepted: 16 July 2021 From Maxwell’s equations in vacuum the velocity of light is related to the magnetic Published: 20 July 2021 permeability m0 and vacuum permittivity #0 through the relation Publisher’s Note: MDPI stays neutral 1 c = p . (1) with regard to jurisdictional claims in #0m0 published maps and institutional affil- iations. Since 20 May 2019, the velocity of light in vacuum c is defined to be c = 299, 792, 458 m/s and #0 and m0 are derived from the measurement of the fine structure constant a: e2 e2cm a = = 0 (2) hc h Copyright: © 2021 by the authors. 4p#0¯ 4p¯ Licensee MDPI, Basel, Switzerland. being e and h¯ also defined. Today’s CODATA value is a−1 = 137.035999206 ± 0.000000011. This article is an open access article Due to the linearity of Maxwell’s equations in vacuum the velocity of light in classi- distributed under the terms and cal vacuum does not depend on the presence of other electromagnetic fields (photons, conditions of the Creative Commons Attribution (CC BY) license (https:// static fields). creativecommons.org/licenses/by/ The formulation of Einstein’s energy-mass relation, Heisenberg’s Uncertainty Princi- 4.0/). ple and Dirac’s relativistic equation of the electron opened the doors to vacuum fluctuations Universe 2021, 7, 252. https://doi.org/10.3390/universe7070252 https://www.mdpi.com/journal/universe Universe 2021, 7, 252 2 of 31 leading to nonlinear electrodynamics in vacuum such as light-by-light (LbL) elastic scatter- ing and vacuum magnetic birefringence (VMB). These two closely related processes are shown in Figure1 using today’s Feynman diagrams. Interestingly, VMB is a macroscopic manifestation of a purely relativistic quantum mechanical effect resulting in a reduction of the speed of light in vacuum in the presence of an external field. Figure 1. Lowest order nonlinear elementary processes in vacuum. (Left) light-by-light elastic scatter- ing. (Right) vacuum magnetic birefringence. QED is an extremely well tested theory but always in the presence of charged par- ticles either in the initial and/or final states. The observation of VMB would represent a fundamental confirmation of QED with only low energy photons in the initial and final states. In the present review paper included in a volume devoted to the Italian Research Infrastructure of relevance for astroparticle physics we will describe the acquired experi- ence with the PVLAS experiment [1] along with its intrinsic limitations. The information presented in this paper is mostly contained in [1]. Here though we only present the most important issues to offer a less cumbersome reading. Moreover, this review also contains new experimental and conceptual developments in the field obtained during the last year. Indeed, a brief introduction will be given to a new optical polarimetric scheme [2] being proposed at CERN [3] and tested at the INFN section of Ferrara which overcomes the limitations of PVLAS. Hopefully, this new scheme will permit the first detection of this challenging, intriguing and fundamental process. An effective Lagrangian density taking into account e+e− vacuum fluctuations was first written by H. Euler and B. Kockel in 1935 [4] and shortly after generalized by H. Euler, W. Heisenberg and V. S. Weisskopf [5–7] in 1936. The Lagrangian LEK was later confirmed within the QED framework [8,9]. For electric and magnetic fields well below their critical 2 3 18 2 2 9 values (E Ecrit = me c /eh¯ = 1.38 × 10 V/m and B Bcrit = me c /eh¯ = 4.4 × 10 T) the resulting free field electromagnetic Lagrangian density was determined to be 2 2 !23 1 E2 A E2 ~E L = − 2 + e − 2 + · ~ + EK 2 B 4 2 B 7 B 5 . , (3) 2m0 c m0 c c where 2 h¯ 3 = 2 = × −24 −2 Ae 4 5 a 1.32 10 T . (4) 45m0 me c It is apparent that LEK, with terms to the 4th power in the fields, admits 4-field inter- actions. The parameter Ae describes the entity of the nonlinear correction to the Classical 2 Lagrangian and a = e /(4pe0hc¯ ) is the fine structure constant. Allowing 4-field interac- tions, this Lagrangian leads to light-by-light (LbL) scattering [9,10], to a reduction of the velocity of light in the presence of an external field and to Vacuum Magnetic Birefringence (VMB) [11–16], namely a difference in the indices of refraction for light polarized parallel ~ and perpendicular to an external magnetic field Bext. As of today LEK still needs direct experimental confirmation at energies below the electron mass. Evidence of LbL scattering of high energy virtual photons has been recently published by the ATLAS collaboration [17] and an indirect evidence of VMB has been published by Mignani et al. [18] (with some criticism [19]) as a result of observations of polarized light from an isolated neutron star. The macroscopic properties of the quantum vacuum in the presence of an external field can be studied through the complex index of refraction nc = n + ik where n is the index of refraction and k is the extinction coefficient describing absorption. Furthermore, Universe 2021, 7, 252 3 of 31 considering the propagation of a linearly polarized beam of light, if nc also depends on the polarization direction then Dn is the birefringence and Dk is the dichroism. By applying the Euler-Lagrange equations to LEK one finds that electromagnetism in the presence of vacuum fluctuations is still described by Maxwell’s equations but in a medium (in the absence of currents and charges) ¶~B r~ · D~ = 0 r~ × ~E = − ¶t (5) ¶D~ r~ · ~B = 0 r~ × H~ = ¶t where the relation between H~ and ~B and between D~ and ~E are given by " ! # ~B ~B A E2 ~E ~E ~ = − ~ = + e − 2 ~ − · ~ H M 4 2 B B 14Ae B (6) m0 m0 m0 c c c E2 D~ = # ~E + ~P = # ~E + A 4 − B2 # ~E + 14# A ~E · ~B ~B . (7) 0 0 e c2 0 0 e These relations result in a nonlinear anisotropic behavior of vacuum. The vectors D~ and H~ are no longer linear in the fields ~E and ~B and the indices of refraction for light polarized parallel and perpendicular to an external magnetic field are nk,? > 1 and nk 6= n? resulting in VMB [12–15]. Considering a beam of linearly polarized light passing through a ~ ~ ~ ~ ~ transverse magnetic field and substituting E = Elight and B = Blight + Bext one finds h i ~ ~ 2 ~ ~ ~ ~ Dlight = #0 Elight − 4AeBextElight + 14Ae Elight · Bext Bext (8) h i ~ 1 ~ 2 ~ ~ ~ ~ Hlight = Blight − 4AeBextBlight − 8Ae Blight · Bext Bext (9) m0 p from which one can determine n = #rmr in the two cases: 2 2 nk = 1 + 7AeBext (EK) 2 −24 Bext 2 ) Dn = 3AeBext = 3.96 × 10 . (10) n? = 1 + 4AeBext 1 T The velocity of light in vacuum in the presence of an external field is less than c and it depends on the polarization direction of the propagating wave: vacuum is predicted to behave as a uniaxial nonlinear crystal. The resulting birefringence predicted by LEK in the presence of an external magnetic field is extremely small [11–16]. Similarly, an electric field could be used to generate a birefringence in which case E 2 n − n = Dn(EK) = −3A ext (11) k ? e c 2 2 but experimentally higher values of Bext can be obtained with respect to (Eext/c) .
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